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An Improved Family of Estimators for Estimating Population Mean Using Robust Regression in the Presence of Outliers

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Abstract

Outliers can be misleading and cause false interpretations of statistical results. Dealing with outliers properly can help with acquiring effective information before drawing a conclusion based on that data. Normality assumption in the traditional least square regression method is one of the standard statistical assumptions that is affected by outliers. Robust regression is a method for estimating regression coefficients in the linear regression model with contaminated data that has outliers in it in order to improve the efficiency of the estimators. In this paper, a family of estimators for finite population mean using robust regression with known parameters of an auxiliary variable that is related to the study variable has been proposed. Expression of the bias and mean square error of the improved family of estimators has been demonstrated using a Taylor series approximation. The simulation studies measure the efficiency of the proposed family of estimators for estimating population mean using the mean square error as a criterion. The simulation results show that the improved family of estimators work well under suitable conditions.

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Funding

This research was funded by Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Thailand contract no. 651103. Thank you to all the unknown referees for their valuable comments which help to improve this paper.

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Authors and Affiliations

  1. Department of Applied Statistics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, 10800, Bangkok, Thailand

    Nuanpan Lawson

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  1. Nuanpan Lawson
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Correspondence to Nuanpan Lawson.

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(Submitted by W. Bodhisuwan)

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Lawson, N. An Improved Family of Estimators for Estimating Population Mean Using Robust Regression in the Presence of Outliers. Lobachevskii J Math 43, 3368–3375 (2022). https://doi.org/10.1134/S1995080222140220

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  • DOI: https://doi.org/10.1134/S1995080222140220

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